Reference no: EM132022966

Approximating Bond Price Changes Using Duration and Convexity Rules A 30-year maturity bond making annual coupon payments with a coupon rate of 15.5% has duration of 11.25 years and convexity of 182.9. The bond currently sells at a yield to maturity of 8%. a. Find the exact price of the bond if its yield to maturity falls to 7%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of the bond $ 1744.96 b. Assume that you need to make a quick approximation using the duration rule (instead of the exact calculation in part a above). What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Predicted price $ 1548.65 c. Assume that you need to make a quick approximation using the duration-with-convexity rule (instead of the exact calculation in part a above). What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Predicted price $ 1550.48 d-1. What is the percent error for each rule? [Hint: percent error is the deviation from the exact price, divided by the exact price. It indicates the extent to which the approximated price differs from the exact price. A smaller percent error indicates more precise approximation.] (Enter your answer as a positive value. Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.) Percent Error YTM Duration Rule Duration-with- Convexity Rule 7% 2.75 % 2.64 % d-2. What do you conclude about the accuracy of the two rules? The duration rule provides more accurate approximations to the actual change in price. The duration-with-convexity rule provides more accurate approximations to the actual change in price. e-1. Find the exact price of the bond if it's yield to maturity rises to 9%. (Do not round intermediate calculations. Round your answer to 2 decimal places.) Price of the bond $ e-2. What price would be predicted by the duration rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Predicted price $ e-3. What price would be predicted by the duration-with-convexity rule? (Do not round intermediate calculations. Round your answer to 2 decimal places.) Predicted price $ e-4. What is the percent error for each rule? (Do not round intermediate calculations. Round "Duration Rule" to 2 decimal places and "Duration-with-Convexity Rule" to 3 decimal places.) Percent Error YTM Duration Rule Duration-with- Convexity Rule 9% % % e-5. Are your conclusions about the accuracy of the two rules consistent with parts (a) – (d)? Yes No